Find all n ∈ Z for which 3x^2 + 2nx + 12 is irreducible over Q.

Q: O IS the set Of all postive inTaYs CIOScd for subtraction?is t st of all positive intagars closed…

A: 8. A. Consider the set of all positive integers. Take 2 positive integers, say 5 and 11. Subtracting…

Q: A population consists of 4 units with values 156, 149, 164 and 155 respectively. Draw all possible…

A: Given that Population size N = 4 Sample size n = 2 Then possible samples WOR are NCn = 4C2 = 6

Q: is intea rable Primitive aR 2 > X 3 1 2. 1 ラメラ 。 (今さ うx 31 ラ× %3D >入う。

A: we have Fx=0            0≤x<12x-1    1≤x≤2and fx=1     0≤x≤12    1≤x≤2 i The primitive of a…

Q: Find inverse Z-transform 1+- X(z) = (1 - -)*

A:

Q: Evaluate the integral. '3 dt 1

A:

Q: Find all exact sdutions on [o,2T] (Gnter your 90swer in a comma seperated list tan (x)-25itan(x)= 0

A:

Q: rivial of

A: To find the non trivial of Z8 as,

Q: * find z- transform for -4 x (n) = { 2 1 2 3} x(2) = 2 +z + 2z-2 + 3z-3 x(2) = 222 + z +=+ 2 + 3Z'…

A:

Q: Compute Ax by dot product. 2 10 1 2 1 0 0 1 0 0 1 2 1 2 1 1 2

A:

Q: Show that both ℝ and ℝ2 may be covered by countably many open balls.

A:

Q: Show that, cosh-1 x = In (x + /x² – 1)|

A:

Q: 5. Prove OR disprove that Z/2ZOZ/3Z is isomorphic to Z/6Z

A: To prove or disprove that  Recall that , Now to prove or disprove that  These elements of these…

Q: find all the Second order partial denvatives of the givén funcion fua、り) %3D

A: The given function is f(x,y)=exy

Q: The set of integers is not dense in cofinite topo log y of R True False O

A: The set of integers is not dense in co finite topology on ℝ.

Q: 3dz 1. S 4-5z

A:

Q: In Z3×U3, Find the order of (1, 2). Show your work.

A:

Q: (List all irreducible polynomials of degree < 2 in Z3 [x].

A:

Q: Show that if x, y,z are positive integers then: z-gcd (x,y) = gcd(zx ,zy)

A: The greatest common divisor (gcd) is the largest positive integer that divides each of the integers…

Q: 3. Solve for the Z-Transforms and ROCs of: x[n] = [6, -2,2,0,0,4, -3]

A: We have to solve the given problem.

Q: 4) State the Rank-Nullity Theorem.

A: To state: Rank - Nullity theorem.

Q: The number of reducible monic polynomials of degree 2 over Zz is

A: The number of reducible monic polynomials of degree 2 over Z3 is

Q: Prove that 1- coshx=In(x+ -x=In(x + Vx² -1 |

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: Show that - In(x – V - 1) = In(x + Vr – 1)

A:

Q: Compute In(z) dr.

A:

Q: Orthonormalize the set {(¿).(9)} with respect to the inner product from before.

A:

Q: Find the order of [5] in Z23 using Fermat's Theorem.

A:

Q: Compute the following integral: / secʻ(5x) tan" (5x) de 1 (tan(5x))*+3 + C 1 а) 5R + 5 (tan(5x))*+1…

A: We can solve this by using some basic concept of integration as substitution method .

Q: In (a le) secx ((2- sec²x) " sec (3А - x) to be integrable using the formula What should be the…

A:

Q: Find all monic irreducible polynomials of degree 2 over Z

A: A polynomial of degree 2 in Z3 [x] is irreducible if and only if it has no roots in Z3.

Q: Evaluate the integral: Sen(1²2+3x-7) е dx A x² + 5x+In 3x-6|+C XZ B +5x+31n|x-2|+C 2 C x ²2+ = +…

A: On solving this we will get

Q: Solve for DE: separable DE

A:

Q: is Flaiy)= integrahing an 2

A:

Q: Use (3) from Section 5.4 to evaluate the integral: -7/9 dx %3D 4.

A: Given integration is : ∫47x-79dx To find the value of integration.

Q: Prove that In( +VI-X²³) = In ( ¹+ √1-x²) sech ¹(x) =

A:

Q: Demonstrate that x' + 3x – 8 is irreducible over Q. -

A: Given function is fx=x3+3x2−8 We have to show that fx=x3+3x2−8 is irreducible over Q(Rational…

Q: Find the Fourier integral foxx) 5 if -25X TO -8 iP xx2

A:

Q: Show that 1 sech-1x = In x2

A:

Q: Evaluate the double integral ſ IN ydxdy.

A:

Q: 3 has infinitely many soluti

A:

Q: Calculate the definite integral goven belaw 2 3x- 3 x2 - 2x + 6 -2

A: Using substitution method

Q: 8. S(1- sec3x)²dx

A:

Q: The term r ryis homogenous of degree two. -

A:

Q: 3)(2x-ズ) ax

A: First I have split the integral in two parts then just use the rule of integral and find the…

Q: Express x8. -x over Q[æ] and over F2[x] as a product of irreducible

A: Let f(x) = x8 — x. Over Q,f(x) = x(x7 — 1) = xϕ1xϕ7x=xx-11+x+...+x6 Note that  ϕ1x and ϕ7x are…

Q: 5. Evaluate the integral JI. dA, R = [-2, 4] × [1, 3]. R

A:

Q: Express x8-x as a product of irreducibles over Z2

A: We have to express x8-x as a product of irreducible over Z2. Definition:- Irreducibility is defined…

Q: Find the interval and radius of conv. of In(1 – x²)

A: The power series representation of given function ln1-x2 is given by: ln1-x2=∑n=1∞-x2nn

Q: Prove that 1- cosh-x= In(x+ V?-1 x= In(x+Vx² -1

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find all monic irreducible polynomials of degree 2 over Z3.

A:

Q: Prove that: 3-4x² dx 4VIn3

A: The given integral is I=∫0∞3-4x2dx. The idea is to evaluate the above integral using gamma function.…